Budapest is a very nice city--good food, good museums, churches, nice parks (Margit Island, the Buda hills), etc. Lots of culture (opera, etc.) depending on the season.

The nicest hotel is the Four Seasons but the Hilton (Castle District) has a nice view of the Danube and Pest and the IC, the Marriott, and the Sofitel all have nice views of the Danube and Buda (castle hill). Most of the other chain hotels are also quite good (the Le Meridien, the Kempinski, the Hilton West End but with no view although the first two are close to the river and the sights) and there are plenty of Mercures, Novotels, Best Westerns, etc. in the mid range. Avoid the Holliday Inn since it is in the far western suburbs. The other recommendations for small independant places are also fine.

Transport is easy (busses, trams, three metros) and you can buy individual tickets (as mentioned, you need a new one every time you change), day passes, three days passes, week passes. Taxis are also reasonable (City especially but Fo is good, too) and Zona Taxi from the airport is a good deal--with two or more people it is cheaper than the mini-bus. I would avoid public transport from the airport (meaning the city bus to the metro to another bus) unless you are really adventurous and have very little luggage. The biggest problem is taxis from the train stations, since they are often scam artists, but it's harder to get around this.

Like any big city in Europe, you have to be careful of pick pockets, etc. but in general, it is MUCH safer than a comparably sized city in the US (Philadelphia, Houston).